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Question
If A and B are two events such that `P(A) = 1/4, P(B) = 1/2 and P(A ∩ B) = 1/8`, find P (not A and not B).
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Solution
As `P (A cap B) = 1/8 = 1/4 xx 1/2 = P (A) xx P (B)`
⇒ A and B are independent.
⇒ Ac and Bc are also independent.
⇒ P (Ac ∩ Bc) = P (Ac) P (Bc)
⇒ P (Ac ∩ Bc) = (1 - P(A)) (1 - P (B))
`= (1 - 1/4) (1 - 1/2) = 3/4 xx 1/2 = 3/8`
(∴ P (Ac) = 1 - P (A) & P(Bc) = 1 - P (B))
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